Slice the flank steak against the grain into thin, bite-sized strips and season them evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, rice vinegar, and toasted sesame oil until well combined.
Heat a large stainless steel skillet or cast-iron wok over medium-high heat until a drop of water sizzles on contact.
Add the steak strips to the hot pan in a single layer, searing for 2-3 minutes until a deep golden crust forms, then transfer to a clean plate.
Place the broccoli florets into the same pan with two tablespoons of water, covering with a lid for 2 minutes to steam until bright green and tender-crisp.
Remove the lid, push the broccoli to the sides, and add the minced garlic and grated ginger to the center, sautéing for 30 seconds until aromatic.
Return the seared beef and any accumulated juices to the pan, pouring the prepared sauce over the ingredients.
Toss everything continuously for 1 minute to coat the beef and broccoli in the thickening glaze.
Garnish with sesame seeds and serve immediately for peak flavor and texture.